Advisors

Now showing items 1-8 of 8

    • 2-fold structures and homotopy theory 

      Haderi, Redi (Bilkent University, 2023-01)
      It is well-known that correspondences between categories, also known as profunctors, serve in classifying functors. More precisely, every functor F : X → A straightens into a lax mapping χF : A → Catprof from A into a ...

    • Cobordism calculations with Adams and James spectral sequences 

      Erdal, Mehmet Akif (Bilkent University, 2010)
      Let ξn : Z/p → U(n) be an n-dimensional faithful complex representation of Z/p and in : U(n)→O(2n) be inclusion for n ≥ 1. Then the compositions in ◦ ξn and jn ◦ in ◦ ξn induce fibrations on BZ/p where jn : O(2n) → O(2n ...

    • Concrete sheaves and continuous spaces 

      Özkan Recep (Bilkent University, 2015)
      In algebraic topology and differential geometry, most categories lack some good ”convenient” properties like being cartesian closed, having pullbacks, pushouts, limits, colimits... We will introduce the notion of continuous ...

    • A conjecture on square-zero upper triangular matrices and Carlsson's rank conjecture 

      Şentürk, Berrin (Bilkent University, 2018-09)
      A well-known conjecture states that if an elementary abelian p-group acts freely on a product of spheres, then the rank of the group is at most the number of spheres in the product. Carlsson gives an algebraic version ...

    • Finite p-subgroups of Sp(n) 

      Çetin, Mustafa Seyyid (Bilkent University, 2021-09)
      Hikari [1] classifies all finite p-subgroups of simple algebras, and Banieqbal [2] classi-fies the finite subgroups of 2×2 matrices over a division algebra of characteristic zero. In this thesis, we give a new proof for the ...

    • Free actions on CW-complexes and varieties of square zero matrices 

      Şentürk, Berrin (Bilkent University, 2011)
      Gunnar Carlsson stated a conjecture which gives a lower bound on the rank of a differential graded module over a polynomial ring with coefficients in algebraically closed field k when it has a finite dimensional homology ...

    • The geometry of sheaves on sites 

      Parsizadeh, Pejman (Bilkent University, 2021-01)
      In this work, we study doing geometry on sheaves on sites. Categories of our sites consist of objects that are building blocks for a given geometry. Generalized spaces then will be sheaves on these sort of sites. Next we ...

    • Monoid actions, their categorification and applications 

      Erdal, Mehmet Akif (Bilkent University, 2016-12)
      We study actions of monoids and monoidal categories, and their relations with (co)homology theories. We start by discussing actions of monoids via bi-actions. We show that there is a well-defined functorial reverse action ...